Investment Decisions with Births and Deaths

Most Real Options authors have been assuming that the only critical variable in the investment decision analysis is price. The success of an investment depends not only on the price of a product but also on other variables like the quantity of production. The number of units sold is a variable with different characteristics than price. It can be in some applications a discrete variable, and its drift and volatility can be affected by different factors. We present a model in which a monopoly investor has the option to invest in a new market, in which the number of units sold follows a stochastic birth and death process. We present a numerical solution for the value of the option to invest and for the trigger level for investment. Also we study the sensitivity of the option value to changes in the number of units sold and also the sensitivity of the trigger level to changes in volatility. The model suggests, that the classical assumption of Geometric Brownian motion, as the stochastic process of the underlying variable can overestimate the option value to invest.